In February, Mr. Bates was charged with murder, and as part of the investigation, the police sought from Amazon “electronic data in the form of audio recordings, transcribed words, text records and other data” captured by the Echo.

The request has raised concern among some right-to-privacy supporters.

Marc Rotenberg, president of the Electronic Privacy Information Center, said in an email that there should be a “clear legal standard that governs law enforcement access” to machines that make up what has become known as the internet of things. The reference is to the constellation of devices — such as cameras, cellphones and appliances — connected to the internet.

But Lynn Terwoerds, the executive director of the Executive Women’s Forum, which founded and sponsors the Voice Privacy Alliance, said in an email that the request for the information was built on a faulty premise.

She said the Echo is always listening for a “wake word” — Alexa, Amazon or another customizable term — and records only what is said after it has been activated. She said it has 60 seconds of recorded sound in its storage. “What this ‘always listening’ means is that the device is not eavesdropping and interpreting everything you’re saying,” Ms. Terwoerds wrote.

Once it detects the wake word, according to Amazon, the Echo starts streaming audio to the cloud, where it is secured until the customer permanently deletes it.

The case raises “serious privacy concerns with this kind of nonspecific warrant,” Ms. Terwoerds said, adding, “We have to fight against the myth of Echo listening in on our every word and sending that data to Amazon — it’s simply untrue.”

Jon Simpson, the police chief in Bentonville, which, by car, is about three hours northwest of Little Rock, referred questions to Nathan Smith, the prosecuting attorney in Benton County. In an email, Mr. Smith said Amazon had yet to fully comply with two requests, although he said it had provided “some very limited subscriber information.”

The company said in a statement that it would not “release customer information without a valid and binding legal demand properly served on us.” Mr. Smith said that officers had followed the proper procedure in seeking a search warrant from a judge based on probable cause, and that he hoped Amazon would comply and that no further steps would be necessary.

While many right-to-privacy supporters have expressed interest in the request, Mr. Smith said the case was “ really about seeking justice for the victim.” He added that it was the responsibility of the police to seek the data to determine its relevance to the investigation. A lawyer for Mr. Bates did not respond to an email and a phone call seeking comment.

The Arkansas case is reminiscent of an episode in which the federal government sought to legally compel Apple to unlock an iPhone used by a gunman in a shooting in San Bernardino, Calif., last year that killed 14 people. The case became contentious as Apple refused to assist the authorities, prompting a debate about whether privacy or security was more important. Federal officials said in March that they found a way to unlock the phone without help from Apple.

The lack of clear-cut legislation over who is legally entitled to the data from such devices means these kinds of cases will continue to surface, Mark A. Testoni, the president and chief executive of SAP National Security Services, which helps agencies track those suspected of terrorism through open source data, said in an interview.